GeekDad Puzzle of the Week: Maximize Bedtime Utility

In the language of economics, bedtime at my house is a zero sum game — my kids’ gains borne of staying up any extra minutes are exactly balanced by my wife’s and my losses from same. So what’s the optimal bedtime? I posit it’s the time that maximizes family utility: late enough to be reasonable, but early enough so that my wife and I don’t go stark raving mad. For example, it’s a complete nonstarter to suggest bedtime before Sprout’s Good Night Show host Nina (who, coincidentally, is a zombie) does Lucy Light My Way at 7:30pm. And my wife and I become werewolves at 9:30pm sharp.

Between those two times is some wiggle room. Our optimal bedtime wiggles according to the following rules:

• Every book read is worth 10 minutes in utility to my kids. However, while the first book costs my wife and I only 2 minutes of utility, every subsequent book costs another additional minute.

• Asking to play chess gains my 5yo 30 initial minutes of utility, which, unfortunately, decays at a rate of 1minute-per-1minute, as while we play chess, my 3yo bugs my wife who would otherwise be hiding in the back room re-watching West Wing DVDs on her laptop.

• The kids have learned that we feel guilty about neglecting our yellow lab, Gus, whom we had before we had kids. Kids earn 16 minutes of utility by offering to pet Gus and tell him he’s a good dog. Every subsequent offer earns them the square root of the previous utility.

What’s our optimal bedtime? Really — I’d love to know!

Send your answers to GeekDad Puzzle Central by the end of the day on Friday for your chance to win a $50.00 ThinkGeek Gift Certificate and my eternal gratitude.